# Actually Integer Metagolf

## Background

Actually (the successor to Seriously) is a stack-based imperative golfing language I created in November of 2015. Like many other golfing languages, it has one-byte commands that perform different functions based on the contents of the stack. One of its specialties is mathematics - it has a wide variety of mathematics-based commands. However, in order to perform math operations, you have to put (one or more) numbers on the stack. Pushing a specific value in as few bytes as possible is tricky, because there are many different options. In this challenge, you will be doing exactly that: representing numbers (specifically, integers) in Actually in as few bytes as possible.

## The Challenge

Given an integer N as input, output valid Actually code that results in N being pushed to the stack.

• The input will be within the range of a 32-bit signed two's complement integer (i.e. the integers in the inclusive range [-2147483648, 2147483647]).
• The result must be an integer (not a float, string, list, or function), and must be on top of the stack.
• You may not make any assumptions about the contents of the stack (like whether or not it is empty). Any existing values on the stack must not be modified or rearranged.
• The latest commit of Actually at the time I am writing this challenge is to be used. If I make bug fixes or performance enhancements (or any other minor change that does not remove or change functionality of the allowed commands), I will update this version.
• Your solution must do at least as well as the trivial solution (prepend : to the input to make a numeric literal).
• Your score will be the sum of the lengths of the trivial solutions minus the sum of the lengths of the outputs for the selection of 1000 32-bit signed two's complement integers used for scoring, which can be found below. I reserve the right to change the scoring integers at any time, if there is a need (such as optimizing for the test cases or the test cases not being thorough enough).
• Solutions must output a valid answer within 30 seconds for each input. Timing will be done on a standard free Cloud9 workspace.

## Commands

For simplicity, only 141 out of the (currently) 208 commands may be used, and many overloads of those 141 that are unrelated to number-crunching have been removed. Here is the list of allowed commands (format is <hex code> (<symbol>): <descriptions of functions based on stack values and types>:

0B (♂): take the next command and map it over the top of the stack (for example, ♂A is equivalent to AM)
1F (▼): pop a,b: push b//gcd(a,b),a//gcd(a,b); pop [a]: push [x//gcd([a]) for x in [a]]
20 ( ): push the # of elements on the stack (push len(stack))
21 (!): pop a: push a! (factorial(a))
22 ("): string literal, reads until next " and pushes value onto stack. An implied " is present at EOF if needed.
23 (#): pop a: push list(a)
25 (%): pop a,b: push a%b
26 (&): pop a,b: push a & b (bitwise AND)
27 ('): pushes next character onto stack as character literal (length-1 string)
28 ((): rotates stack right by 1
29 ()): rotates stack left by 1
2A (*): pop a,b: push a*b; pop a,[b] or [b],a: apply a* to each element in the array; pop [a],[b]: push dot product of [a] and [b] (sum([a[i]*b[i] for i in len(a)])) (shorter is padded with 0s)
2B (+): pop a,b: push a+b; pop [a],[b]: push [a][b] (append [b] to [a]); pop a,[b] or [b],a: apply a+ to each element in the array
2D (-): pop a,b: push a-b; pop [a],[b]: push [a]-[b] (all elements of [a] not in [b])
2F (/): pop a,b: push a/b (float division); pop [a]: rotate [a] right by 1, push [a]
30 (0): push 0
31 (1): push 1
32 (2): push 2
33 (3): push 3
34 (4): push 4
35 (5): push 5
36 (6): push 6
37 (7): push 7
38 (8): push 8
39 (9): push 9
3A (:): numeric literal delimiter: pushes the longest string of characters in '0123456789+-.ij' as a numeric
3B (;): pop a: push a,a (duplicates top element)
3C (<): pop a,b: push 1 if a<b else 0
3D (=): pop a,b: push 1 if a==b else 0
3E (>): pop a,b: push 1 if a>b else 0
40 (@): pop a,b: push a,b (rotate top 2 elements)
41 (A): pop a: push abs(a)
43 (C): pop a: push cos(a)
44 (D): pop a: push a-1; pop [a]: push stddev([a])
45 (E): pop a: push erf(a); pop [a],b: push [a][b] (bth item in [a])
46 (F): pop a: push Fib(a) (Fib(0)=0, Fib(1)=Fib(2)=1); pop [a]: push a[0]
48 (H): pop [a],b: push [a][:b]
49 (I): pop a,b,c: push b if a is truthy, else push c
4B (K): pop a: push ceil(a)
4C (L): pop a: push floor(a)
4D (M): pop f,[a], execute f for each element in [a], using the element as a temporary stack, push [a] (similar to map(f,[a])); pop [a]: push max([a])
4E (N): pop [a]: push a[-1]
50 (P): pop a: push the a-th prime (zero-indexed)
52 (R): pop f,[a]: call f, using [a] as a temporary stack, push [a] (similar to reduce(f,[a])); pop [a]: push [a][::-1] (reverse); pop a: push [1,2,...,a] (range(1,a+1))
53 (S): pop a: push sin(a); pop [a]: push sorted(a)
54 (T): pop a: push tan(a); pop [a],b,c: set [a][b] to c, push [a]
55 (U): pop [a],[b]: push union of [a] and [b]
57 (W): loop delimiter: peek top of stack, repeat code in loop while a evaluates to true
59 (Y): pop a: push !bool(a) (logical negate, opposite of b)
5A (Z): pop [a],[b]: push zip([a],[b]); pop a, zip the next a lists
5B ([): begin list literal, values are delimited by commas (,)
5C (\): pop a,b: push a/b (integer division); pop [a]: rotate [a] left by 1, push [a]
5D (]): end list literal
5E (^): pop a,b: push a XOR b
5F (_): pop a: push ln(a)
60 (): function literal delimiter, pushes function whose body contains all of the commands until the next . An implied  is present at EOF if needed.
61 (a): invert the stack ([a,b,c,d] -> [d,c,b,a])
62 (b): pop a: push 0 if a==0 else 1; pop "a" or [a]: push 0 if len(a)==0 else 1; pop f: push 0 if len(f)==0 else 1
63 (c): pop a: push character at ordinal a%256; pop [a],b: push [a].count(b)
64 (d): pop [a]: dequeue b from [a], push [a],b
65 (e): pop a: push exp(a)
66 (f): pop a: push the Fibonacci index of a if a is a Fibonacci number, else -1
67 (g): pop a,b: push gcd(a,b); pop [a]: push gcd([a])
68 (h): pop a,b: push sqrt(a*a+b*b) (Euclidean norm)
69 (i): pop [a]: push each element from [a], starting from end (flatten)
6B (k): pop all elements from stack, convert to list (in the order they were on the stack, starting from the top), and push
6C (l): pop [a]: push len([a])
6D (m): pop a: push int(a),frac(a) (modf(a)); pop [a]: push min([a])
6E (n): pop a,b: push a b times
6F (o): pop [a],b: push b to [a], push [a]
70 (p): pop a: push 1 if a is prime else 0; pop [a]: pop b from [a], push [a],b
71 (q): pop [a],b: enqueue b in [a], push [a]
72 (r): pop a: push [0,1,...,a-1] (range(0,a))
75 (u): pop a: push a+1
77 (w): pop a: push the full positive prime factorization of |a| (18 -> [[2,1],[3,2]], -5 -> [[5,1]])
78 (x): pop a,b: push [a,b) (range(a,b)); pop [a]: push range(*a)
79 (y): pop a: push the positive prime factors of |a| (18 -> [2,3], -5 -> [5])
7B ({): pop a: rotate stack right a times
7C (|): pop a,b: push a | b (bitwise OR)
7D (}): pop a: rotate stack left a times
7E (~): pop a: push ~a (unary bitwise negate)
80 (Ç): pop a,b: push a+bi; pop [a]: pop pairs of real numerics b,c from [a] and push b+ci (appending 0 to [a] if len([a]) is odd)
83 (â): pop a: push asin(a)
84 (ä): pop a: push acos(a)
85 (à): pop a: push atan(a)
86 (å): pop a,b: push atan2(a,b)
87 (ç): pop a: push asinh(a)
88 (ê): pop a: push acosh(a)
89 (ë): pop a: push atanh(a)
8B (ï): push i, the imaginary unit (sqrt(-1) or 0+1i)
8C (î): pop a, push 0+ai; pop [a], push [a] with every element multiplied by i
8D (ì): pop a: push 1/a
8E (Ä): pop a: push sinh(a)
8F (Å): pop a: push cosh(a)
90 (É): pop a: push tanh(a)
91 (æ): pop [a]: push mean([a])
9A (Ü): pop [a]: push mode([a])
9B (¢): pop a,b: push abs(a)*sgn(b)
9D (¥): pop [a],[b]: push the result of pairwise addition of [a] and [b], padding the shorter with 0s
9E (₧): pop z: push phase(z)
A0 (á): pop z: push the complex conjugate of z
A7 (º): pop a: push degrees(a)
A8 (¿): pop a,b: push int(a,b) (interpret a as a base-b int)
A9 (⌐): pop a: push a+2
AA (¬): pop a: push a-2
AB (½): pop a: push a/2 (float division)
AC (¼): pop a: push a/4 (float division)
AD (¡): pop a,b: push a string representing a in base b
B0 (░): pop [a],[b]: push [[b][i] if [a][i] for i in len(b)], pads [a] with 0s if necessary
B1 (▒): pop a: push totient(a) (# of integers <= a that are coprime with a)
B2 (▓): pop a: push pi(a) (# of primes <= a)
B3 (│): duplicate stack ([a,b,c] => [a,b,c,a,b,c])
B4 (┤): pop a,b: push 1 if a and b are coprime else 0
B9 (╣): pop a: push the ath row in Pascal's triangle
C5 (┼): duplicate each element on stack ([a,b,c] => [a,a,b,b,c,c])
C6 (╞): pop a: make a total copies of each element on stack (3 [a,b,c] -> [a,a,a,b,b,b,c,c,c])
C7 (╟): pop a: pop a elements and push a list containing those elements in their original order
CB (╦): push pi
CC (╠): push e
D1 (╤): pop a: push 10**a
D2 (╥): pop a: push log(a) (log base 10)
D3 (╙): pop a: push 2**a
D4 (╘): pop a: push lg(a) (log base 2)
D5 (╒): push ln(2)
DB (█): pop a,b: push C(a,b) (aCb)
DC (▄): pop a,b: push P(a,b) (aPb)
E2 (Γ): pop a: push Gamma(a)
E3 (π): pop [a]: push product([a])
E4 (Σ): pop [a]: push sum([a])
E7 (τ): pop a: push 2*a
ED (φ): push phi (golden ratio)
F1 (±): pop a: push -a (unary negate)
F2 (≥): pop a,b: push a>=b
F3 (≤): pop a,b: push a<=b
F7 (≈): pop a: push int(a)
F8 (°): pop a: push radians(a)
FB (√): pop a: push sqrt(a)
FC (ⁿ): pop a,b: push pow(a,b)
FD (²): pop a: push a*a

[a] refers to an iterable (list, string, etc.), "a" refers to a string, f refers to a function, and a (and b, and c, and so on) refers to a numeric (or any data type, if the command is type-agnostic).

It is likely that many of these commands will not be used, but I have included them just in case they are useful.

## Scoring

Here are the integers that will be used for scoring:

-2124910654
-2117700574
-2098186988
-2095671996
-2083075613
-2058271687
-2052250777
-2024215903
-2019485642
-2016095616
-2009838326
-2009173317
-2007673992
-2000014444
-1999825668
-1992515610
-1989566707
-1975506037
-1955473208
-1950731112
-1949886423
-1920624450
-1918465596
-1916287469
-1905036556
-1903956118
-1888944417
-1865221863
-1856600057
-1842797147
-1835637734
-1812631357
-1805740096
-1798015647
-1726688233
-1723609647
-1713776890
-1700307138
-1687644479
-1645515069
-1617635994
-1610444000
-1579053372
-1556891649
-1549652116
-1537732956
-1535180388
-1527162056
-1524851611
-1524658412
-1523244369
-1521379172
-1520191198
-1519035741
-1516978241
-1508892332
-1489938422
-1482102944
-1481823232
-1470621147
-1469145091
-1446844485
-1441790509
-1437843276
-1435359182
-1434186947
-1429816311
-1429393781
-1419752032
-1400387846
-1385152926
-1372620863
-1369257355
-1361933674
-1360480816
-1334846204
-1323741718
-1323660173
-1312800992
-1308824840
-1304658551
-1287829999
-1283767920
-1276288210
-1264275838
-1263965596
-1262866901
-1255421887
-1251428680
-1244825786
-1243200329
-1235305532
-1233977691
-1220537074
-1214100716
-1199414474
-1190725823
-1190401800
-1178717689
-1172378149
-1147869245
-1142875190
-1138538768
-1137864183
-1124917489
-1102987222
-1095920186
-1083001017
-1080902655
-1047122002
-1031842676
-1029877334
-1020849489
-1001684838
-998419619
-990915088
-985235989
-982515261
-979074894
-974195629
-973832940
-965324937
-944246431
-938387588
-933873331
-932692878
-928039285
-927947459
-914008773
-907981688
-906376330
-903502449
-898112547
-887444438
-862658502
-843628573
-822463032
-786051095
-776932426
-776033951
-752042328
-746532472
-743149468
-740225710
-734414418
-725435852
-708101516
-699674783
-694869277
-693246525
-690571518
-689249770
-688581912
-686864294
-681445866
-647992869
-641101583
-631409299
-624686189
-613079884
-593711206
-591688546
-591331185
-574790069
-573024823
-565387051
-565137163
-556338668
-556291492
-541411509
-538932064
-500479857
-482419890
-468050561
-424532545
-420534171
-408741873
-406973874
-387664799
-382084509
-367095703
-352332569
-352195997
-346430007
-324596389
-320119776
-306594578
-305952425
-283718911
-267302378
-243302738
-242955859
-232180029
-225394407
-217418127
-212286453
-208344820
-191300139
-186177744
-175765723
-161763935
-157025501
-140389149
-132298608
-126175769
-70566352
-68748576
-53985905
-52674668
-50228620
-39678495
-19825663
-8349922
-8186722
-8125700
-8073135
-8043230
-7994382
-7874433
-7863624
-7784916
-7782477
-7696343
-7607278
-7531250
-7388060
-7368780
-7367625
-7353084
-7334489
-7281141
-7267149
-7140057
-7119066
-7010389
-6992089
-6975258
-6863360
-6784772
-6741079
-6585985
-6550401
-6520011
-6495144
-6459702
-6294273
-6178342
-6169344
-6139663
-6090928
-6022637
-5992707
-5971334
-5925304
-5880940
-5873707
-5807953
-5703992
-5692895
-5535131
-5488812
-5468330
-5404148
-5290247
-5274221
-5264144
-5234715
-5224048
-5179837
-5084014
-5043990
-5028537
-5011679
-4998333
-4922901
-4880159
-4874060
-4787390
-4749096
-4736217
-4502308
-4480611
-4424319
-4363262
-4349743
-4290050
-4240069
-4239657
-4174072
-4093051
-4045363
-4037689
-4033352
-3839265
-3766343
-3716899
-3680075
-3679053
-3581776
-3539227
-3461158
-3282526
-3205947
-3183427
-3169708
-3166430
-3089822
-3061531
-2947574
-2930733
-2919246
-2872882
-2830770
-2739228
-2713826
-2634018
-2613990
-2525529
-2439507
-2432921
-2376201
-2335005
-2307524
-2265548
-2176176
-2123133
-2108773
-2105934
-2075032
-2073940
-2045837
-2045648
-1978182
-1945769
-1935486
-1881608
-1654650
-1602520
-1506746
-1505294
-1475309
-1457605
-1327259
-1312217
-1178723
-1027439
-880781
-833776
-666675
-643098
-593446
-468772
-450369
-443225
-418164
-402004
-319964
-307400
-279414
-190199
-176644
-66862
-32745
-32686
-32352
-32261
-32035
-31928
-31414
-31308
-30925
-30411
-29503
-29182
-28573
-28500
-28093
-27743
-27716
-27351
-27201
-26834
-25946
-25019
-24469
-24341
-24292
-24151
-23732
-22769
-22242
-22002
-20863
-20762
-20644
-20189
-20009
-19142
-19036
-18980
-18616
-18196
-18123
-17942
-17915
-17601
-17494
-16669
-16417
-16317
-15051
-14796
-14742
-14600
-14443
-14159
-14046
-13860
-13804
-13745
-13634
-13498
-13497
-12688
-12471
-12222
-11993
-11467
-11332
-10783
-10250
-10114
-10089
-9930
-9434
-9336
-9128
-9109
-8508
-8460
-8198
-8045
-7850
-7342
-7229
-6762
-6302
-6245
-6171
-5957
-5842
-4906
-4904
-4630
-4613
-4567
-4427
-4091
-4084
-3756
-3665
-3367
-3186
-2922
-2372
-2331
-1936
-1683
-1350
-1002
-719
-152
-128
-127
-124
-122
-121
-119
-116
-113
-112
-111
-107
-104
-102
-101
-100
-95
-94
-91
-90
-87
-81
-80
-79
-78
-73
-72
-69
-68
-66
-65
-63
-57
-54
-52
-51
-48
-47
-46
-45
-43
-41
-37
-33
-31
-30
-27
-25
-21
-18
-15
-12
-8
-1
0
1
3
4
5
6
11
14
17
23
25
26
27
28
29
31
32
39
41
46
49
51
52
56
58
61
64
66
67
70
74
79
80
86
88
89
92
93
99
102
104
109
113
117
120
122
123
127
695
912
1792
2857
3150
3184
4060
4626
5671
6412
6827
7999
8017
8646
8798
9703
9837
10049
10442
10912
11400
11430
11436
11551
11937
12480
13258
13469
13689
13963
13982
14019
14152
14259
14346
15416
15613
15954
16241
16814
16844
17564
17702
17751
18537
18763
19890
21216
22238
22548
23243
23383
23386
23407
23940
24076
24796
24870
24898
24967
25139
25176
25699
26167
26536
26614
27008
27087
27142
27356
27458
27800
27827
27924
28595
29053
29229
29884
29900
30460
30556
30701
30815
30995
31613
31761
31772
32099
32308
32674
75627
80472
103073
110477
115718
172418
212268
242652
396135
442591
467087
496849
675960
759343
846297
881562
1003458
1153900
1156733
1164679
1208265
1318372
1363958
1411655
1522329
1559609
1677118
1693658
1703597
1811223
1831642
1838628
1884144
1931545
2085504
2168156
2170263
2239585
2308894
2329235
2364957
2432335
2435551
2596936
2684907
2691011
2705195
2738057
2851897
2925289
2995414
3051534
3216094
3267022
3271559
3338856
3440797
3638325
3651369
3718696
3724814
3811069
3854697
3866969
3893228
3963455
3984546
4098376
4100957
4128113
4200719
4256344
4286332
4306356
4316314
4438803
4458063
4461638
4552228
4563790
4584831
4607992
4884455
4907501
5045419
5066844
5150624
5157161
5190669
5314703
5337397
5434807
5440092
5502665
5523089
5547122
5566200
5582936
5634068
5690330
5776984
5778441
5818505
5826687
5827184
5885735
6010506
6084254
6131498
6138324
6250773
6292801
6306275
6315242
6331640
6484374
6502969
6545970
6666951
6690905
6763576
6766086
6895048
6912227
6929081
6941390
6978168
7045672
7085246
7193307
7197398
7270237
7276767
7295790
7375488
7472098
7687424
7840758
7880957
7904499
7948678
7974126
8015691
8037685
8112955
8131380
8140556
8142384
8220436
8308817
8331317
22581970
45809129
48103779
78212045
79674901
97299830
110308649
131744428
136663461
138485719
139842794
152061792
152685704
153070991
156228213
164884737
174776199
189346581
193148547
208582124
223891881
227308187
237373798
241214067
242476929
245495851
260606593
275202667
285717038
317009689
322759532
325369206
339724742
340122632
345010859
352375176
355826263
359695034
366118516
370008270
382712922
386379440
401153345
404986391
426084981
442843409
473909474
475192613
492302667
494747879
506279889
509813998
537558350
548423414
548467404
566383324
574188786
574792333
591678147
596558084
597423476
602432742
603067874
629552047
630893263
635249783
644959276
650710927
664859367
669433203
684329599
699991513
714451929
723556530
739294558
750895264
757618344
781123405
796973385
801637715
804776709
829003666
829219068
840167037
854882202
860066192
864304878
864808449
867107161
871871263
880591851
883020336
883178082
920223781
936008673
939417822
956776353
958281059
962183717
964059257
967860573
974322643
974999286
980009921
1032949015
1044249483
1064892676
1075628270
1080848022
1085571657
1173635593
1174809080
1176744978
1209783795
1212074975
1252323507
1254757790
1301450562
1302240953
1314501797
1315121266
1339304157
1364304289
1376260506
1383883477
1395158643
1411117754
1440755058
1448365702
1466814914
1468433821
1490105126
1493912601
1495600372
1509536621
1511014977
1545693948
1548924199
1566583103
1569747154
1574097219
1597784674
1610710480
1618324005
1646105187
1649417465
1655649169
1660619384
1668826887
1671093718
1672456990
1673477565
1678638502
1682302139
1682515769
1687920300
1690062315
1706031388
1713660819
1772170709
1778416812
1833443690
1861312062
1876004501
1876358085
1882435551
1916050713
1944906037
1950207172
1951593247
1973638546
1976288281
1994977271
2020053060
2025281195
2029716419
2033980539
2052482076
2058251762
2069273004
2073978021
2111013213
2119886932
2134609957
2140349794
2143934987

Here is a Python 3 program that can be used to verify and score a submission:

#!/usr/bin/env python3

import shlex
import os
import sys
import subprocess

try:
from seriously import Seriously
except:
print("Unable to load Seriously. Run 'pip3 install seriously' to install it.")
exit()

if len(sys.argv) < 2:
print("Usage: python3 {} 'command_to_call_your_program'".format(sys.argv[0]))
exit()

sys.stdin = open(os.devnull, 'r')

with open('nums.txt') as f:
nums = [int(x) for x in f]

total = 0

for num in nums:
p = subprocess.Popen(shlex.split(sys.argv[1]), stdin=subprocess.PIPE, stdout=subprocess.PIPE, universal_newlines=True)
try:
out = p.communicate(str(num), timeout=30)[0].strip()
except subprocess.TimeoutExpired:
print("Program failed to finish within 30 seconds for {}".format(num))
exit()
val = Seriously().eval(out)[0]
if not len(out) <= len(':'+str(num)):
print("Failed to do at least as well as naive on {} ({})".format(num, out))
exit()
elif val != num or not isinstance(val, int):
print("Incorrect output: {} instead of {}".format(val, num))
exit()
else:
print("{}: {} ({})".format(num, out, len(out)))
total += len(out)

print("Total:", total)
• Can we use persistent data? (Like for storing a bunch of primes, or Fibonacci numbers) – Blue May 17 '16 at 20:30
• "Your solution must do better than the trivial solution, unless the trivial solution is optimal for the given value." for every input? so if my algorithm only does better than the trivial solution 99% of the time, the other 1% disqualify me if any of them are not optimal? – Sparr May 17 '16 at 22:20
• @Blue That is acceptable. – Mego May 18 '16 at 0:36
• @Sparr It means you can't just output the trivial solution if there is a better solution. – Mego May 18 '16 at 0:36
• @ven That's normal. The language's name is Seriously. In this challenge, we are dealing specifically with Seriously v2, which is named Actually. – Mego May 18 '16 at 18:09

## Python 3, 5152 57 bytes saved

This program brute forces its way through a significant number of 1-5 character programs, using a limited set of 54 56 instructions and a lot of pruning based on the state of the stack before adding each new instruction. It takes about one minute to run on my laptop. 6 characters would take hours.

#!/usr/bin/env python3
# -*- coding: cp437 -*-

import os
import sys
import json
import math
import time
import random
import timeit

try:
from seriously import Seriously,chr_cp437,ord_cp437
except:
print("Unable to load Seriously. Run 'pip3 install seriously' to install it.")
exit()

MAXLEN=5
MAX=2**31

future_alphabet=[

chr_cp437(0x4D), #  (M): pop f,[a], execute f for each element in [a], using the element as a temporary stack, push [a] (similar to map(f,[a])); pop [a]: push max([a])
chr_cp437(0x52), #  (R): pop f,[a]: call f, using [a] as a temporary stack, push [a] (similar to reduce(f,[a])); pop [a]: push [a][::-1] (reverse); pop a: push [1,2,...,a] (range(1,a+1))
chr_cp437(0x57), #  (W): loop delimiter: peek top of stack, repeat code in loop while a evaluates to true
chr_cp437(0x60), #  (): function literal delimiter, pushes function whose body contains all of the commands until the next . An implied  is present at EOF if needed.

]

def next_instruction(program,stack):
plen = len(program)
slen = len(stack)
if plen>0 and program[-1]==chr_cp437(0x0B): # introspect the list on top of the stack
maybes = set(next_instruction(program[:-1],[stack[0][0]]))
# print(maybes)
for i in stack[0][1:]:
maybes = maybes & set(next_instruction(program[:-1],[i]))
# print(maybes)
maybes.discard(chr_cp437(0x72)) # no ranges of lists
maybes.discard(chr_cp437(0xB9)) # no pascal rows of lists
return list(maybes)

candidates = []

if plen==MAXLEN-1 and slen>1:
if any(isinstance(x,list) for x in stack):
return [] # lost cause
if slen==2 and isinstance( stack[0], int ) and isinstance( stack[1], int ):
candidates = candidates + [
chr_cp437(0x2A), #  (*): pop a,b: push a*b; pop a,[b] or [b],a: apply a* to each element in the array; pop [a],[b]: push dot product of [a] and [b] (sum([a[i]*b[i] for i in len(a)])) (shorter is padded with 0s)
chr_cp437(0x2B), #  (+): pop a,b: push a+b; pop [a],[b]: push [a][b] (append [b] to [a]); pop a,[b] or [b],a: apply a+ to each element in the array
chr_cp437(0x2D), #  (-): pop a,b: push a-b; pop [a],[b]: push [a]-[b] (all elements of [a] not in [b])
chr_cp437(0x2F), #  (/): pop a,b: push a/b (float division); pop [a]: rotate [a] right by 1, push [a]
chr_cp437(0x5C), #  (\): pop a,b: push a/b (integer division); pop [a]: rotate [a] left by 1, push [a]
]
if stack[0]>1 and stack[0]<int(math.pow(MAX,1.0/3))+1 and stack[1]>2 and stack[1]<int(math.log(MAX)/math.log(3))+1:
candidates.append(chr_cp437(0xFC))  #  (ⁿ): pop a,b: push pow(a,b)
if stack[0]>2 and stack[0]<1000 and stack[1]>2 and stack[1]<stack[0]:
candidates = candidates + [
chr_cp437(0xDB), #  (█): pop a,b: push C(a,b) (aCb)
chr_cp437(0xDC) #  (▄): pop a,b: push P(a,b) (aPb)
]
return candidates

if plen==MAXLEN-1 and slen==1 and isinstance(stack[0],list):
candidates = candidates + [
chr_cp437(0xE3), #  (π): pop [a]: push product([a])
chr_cp437(0xE4)  #  (Σ): pop [a]: push sum([a])
]
return candidates

candidates = candidates + [
chr_cp437(0x30), #  (0): push 0
chr_cp437(0x31), #  (1): push 1
chr_cp437(0x32), #  (2): push 2
chr_cp437(0x33), #  (3): push 3
chr_cp437(0x34), #  (4): push 4
chr_cp437(0x35), #  (5): push 5
chr_cp437(0x36), #  (6): push 6
chr_cp437(0x37), #  (7): push 7
chr_cp437(0x38), #  (8): push 8
chr_cp437(0x39)  #  (9): push 9
]

if plen==0 or (plen>0 and program[-1]!=":"):
candidates.append(chr_cp437(0x3A)) #  (:): numeric literal delimiter: pushes the longest string of characters in '0123456789+-.ij' as a numeric

# if plen>0 and program[-1]==":":
#     candidates.append(chr_cp437(0x2D)) # negative literal coming

if slen>0:
candidates.append(chr_cp437(0xB3)) #  (│): duplicate stack ([a,b,c] => [a,b,c,a,b,c])

if slen>0 and isinstance( stack[0], int ):
candidates = candidates + [
chr_cp437(0x44), #  (D): pop a: push a-1; pop [a]: push stddev([a])
chr_cp437(0x54), #  (T): pop a: push tan(a); pop [a],b,c: set [a][b] to c, push [a]
chr_cp437(0x65), #  (e): pop a: push exp(a)
chr_cp437(0x75), #  (u): pop a: push a+1
chr_cp437(0xA9), #  (⌐): pop a: push a+2
chr_cp437(0xAA), #  (¬): pop a: push a-2
chr_cp437(0xAB), #  (½): pop a: push a/2 (float division)
chr_cp437(0xAC), #  (¼): pop a: push a/4 (float division)
chr_cp437(0xE7), #  (τ): pop a: push 2*a
chr_cp437(0xF1), #  (±): pop a: push -a (unary negate)
chr_cp437(0xFD), #  (²): pop a: push a*a
chr_cp437(0x7E)  #  (~): pop a: push ~a (unary bitwise negate)
]
candidates.append(chr_cp437(0x3B)) #  (;): pop a: push a,a (duplicates top element)
if stack[0]>=0:
if stack[0]<13:
candidates.append(chr_cp437(0x21)) #  (!): pop a: push a! (factorial(a))
candidates.append(chr_cp437(0xD1)) #  (╤): pop a: push 10**a
if stack[0]<32:
candidates.append(chr_cp437(0xD3)) #  (╙): pop a: push 2**a
candidates.append(chr_cp437(0xB9)) #  (╣): pop a: push the ath row in Pascal's triangle
if stack[0]<100:
candidates.append(chr_cp437(0x46)) #  (F): pop a: push Fib(a) (Fib(0)=0, Fib(1)=Fib(2)=1); pop [a]: push a[0]
candidates.append(chr_cp437(0x50)) #  (P): pop a: push the a-th prime (zero-indexed)
if stack[0]<500 and plen<MAXLEN-1:
candidates.append(chr_cp437(0x72)) #  (r): pop a: push [0,1,...,a-1] (range(0,a))

if slen>0 and isinstance( stack[0], float ):
candidates = candidates + [
chr_cp437(0x4B), #  (K): pop a: push ceil(a)
chr_cp437(0x4C)  #  (L): pop a: push floor(a)
]

if slen>0 and isinstance( stack[0], list ) and len(stack[0])>0:
candidates = candidates + [
chr_cp437(0xE3), #  (π): pop [a]: push product([a])
chr_cp437(0xE4)  #  (Σ): pop [a]: push sum([a])
]
candidates.append(chr_cp437(0x69)) #  (i): pop [a]: push each element from [a], starting from end (flatten)
if plen<MAXLEN-2:
candidates.append(chr_cp437(0x0B)) #  (♂): take the next command and map it over the top of the stack (for example, ♂A is equivalent to AM)

if slen>1:
candidates.append(chr_cp437(0x6B)) #  (k): pop all elements from stack, convert to list (in the order they were on the stack, starting from the top), and push

if slen>1 and isinstance( stack[0], int ):
candidates = candidates + [
chr_cp437(0x61), #  (a): invert the stack ([a,b,c,d] -> [d,c,b,a])
chr_cp437(0xC5), #  (┼): duplicate each element on stack ([a,b,c] => [a,a,b,b,c,c])
chr_cp437(0xC7)  #  (╟): pop a: pop a elements and push a list containing those elements in their original order
]
if stack[0]<100:
candidates.append(chr_cp437(0xC6)) #  (╞): pop a: make a total copies of each element on stack (3 [a,b,c] -> [a,a,a,b,b,b,c,c,c])

if slen>1 and isinstance( stack[0], int ) and isinstance( stack[1], int ):
candidates = candidates + [
chr_cp437(0x2A), #  (*): pop a,b: push a*b; pop a,[b] or [b],a: apply a* to each element in the array; pop [a],[b]: push dot product of [a] and [b] (sum([a[i]*b[i] for i in len(a)])) (shorter is padded with 0s)
chr_cp437(0x2B), #  (+): pop a,b: push a+b; pop [a],[b]: push [a][b] (append [b] to [a]); pop a,[b] or [b],a: apply a+ to each element in the array
chr_cp437(0x2D), #  (-): pop a,b: push a-b; pop [a],[b]: push [a]-[b] (all elements of [a] not in [b])
chr_cp437(0x2F), #  (/): pop a,b: push a/b (float division); pop [a]: rotate [a] right by 1, push [a]
chr_cp437(0x5C), #  (\): pop a,b: push a/b (integer division); pop [a]: rotate [a] left by 1, push [a]
]
if stack[0]>1 and stack[0]<int(math.pow(MAX,1.0/3))+1 and stack[1]>2 and stack[1]<int(math.log(MAX)/math.log(3))+1:
candidates.append(chr_cp437(0xFC))  #  (ⁿ): pop a,b: push pow(a,b)
if stack[0]>2 and stack[0]<1000 and stack[1]>2 and stack[1]<stack[0]:
candidates = candidates + [
chr_cp437(0xDB), #  (█): pop a,b: push C(a,b) (aCb)
chr_cp437(0xDC) #  (▄): pop a,b: push P(a,b) (aPb)
]
if stack[1]-stack[0]>0 and stack[1]-stack[0]<500:
candidates.append(chr_cp437(0x78)) #  (x): pop a,b: push [a,b) (range(a,b)); pop [a]: push range(*a)

if slen>1 and (isinstance( stack[0], list ) or isinstance( stack[1], list )):
candidates = candidates + [
chr_cp437(0x2A), #  (*): pop a,b: push a*b; pop a,[b] or [b],a: apply a* to each element in the array; pop [a],[b]: push dot product of [a] and [b] (sum([a[i]*b[i] for i in len(a)])) (shorter is padded with 0s)
chr_cp437(0x2B), #  (+): pop a,b: push a+b; pop [a],[b]: push [a][b] (append [b] to [a]); pop a,[b] or [b],a: apply a+ to each element in the array
chr_cp437(0x2D), #  (-): pop a,b: push a-b; pop [a],[b]: push [a]-[b] (all elements of [a] not in [b])
chr_cp437(0x2F), #  (/): pop a,b: push a/b (float division); pop [a]: rotate [a] right by 1, push [a]
chr_cp437(0x5C), #  (\): pop a,b: push a/b (integer division); pop [a]: rotate [a] left by 1, push [a]
]

return candidates

# p = "8"+chr_cp437(0x72)+chr_cp437(0x0B)
# res = Seriously().eval(p)
# print(p)
# print(res)
# print(next_instruction(p,res))
# sys.exit()

programs = [[['',None]]]
best = {}

def l(n,force_colon=False):
if force_colon:
return ':'+str(n)
if n>=0 and n<10:
return str(n)
elif n<0 and n>-10:
return str(-n)+'±'
return ':'+str(n)

def cand(n,rep):
# print(n,rep,len(rep),l(n),len(l(n)),best[n] if n in best else "")
if n<=MAX and n>=-MAX and (len(rep)==1 or len(rep)<len(l(n))) and (n not in best or len(rep)<len(best[n])):
best[n] = rep
# print("woot")
return True
return False

for proglen in range(0,MAXLEN+1):
print(proglen,"/",MAXLEN)
if proglen<MAXLEN:
programs.append([])
first = ""
for p in programs[proglen]:
try:
if first!=p[0][0]:
first=p[0][0]
print(" ",p[0][0],"/",9)
except:
pass
if chr_cp437(0x7E) in p[0]:
print(p[0])
now = time.clock()
try:
res = Seriously().eval(p[0])
elapsed = time.clock()-now
if elapsed>0.0005:
timed = timeit.timeit('Seriously().eval("'+str(p[0].encode('unicode_escape'))+'")','from seriously import Seriously',number=1000)
if elapsed>0.01:
print("SLOW:")
print(p[0])
print(res)
print(elapsed)
if chr_cp437(0x7E) in p[0]:
print(res)
if len(res)==1 and isinstance( res[0], int ):
# print("cand",res[0],p[0])
cand(res[0],p[0])
p[1] = res
if proglen<MAXLEN:
# bail out if the stack is too complex to collapse in time
if proglen==MAXLEN-1:
if len(res)>0 and isinstance( res[0], list ) and not isinstance( res[0][0], int ):
continue
if len(res)>1 and isinstance( res[0], list ):
continue
if len(res)>2:
continue
for c in next_instruction(p[0],res):
programs[proglen+1].append([p[0]+c,None])
except:
pass

# print(programs)

def best_or_l(n,force_colon=False):
if n in best:
return best[n]
if n<0 and -n in best:
return best[-n]+chr_cp437(0xF1)
return l(n,force_colon)

# for key,value in sorted(best.items()):
#     # if random.random()<0.01:
#     print(key,value)

score = 0
for i in [-2124910654, -2117700574, -2098186988, -2095671996, -2083075613, -2058271687, -2052250777, -2024215903, -2019485642, -2016095616, -2009838326, -2009173317, -2007673992, -2000014444, -1999825668, -1992515610, -1989566707, -1975506037, -1955473208, -1950731112, -1949886423, -1920624450, -1918465596, -1916287469, -1905036556, -1903956118, -1888944417, -1865221863, -1856600057, -1842797147, -1835637734, -1812631357, -1805740096, -1798015647, -1726688233, -1723609647, -1713776890, -1700307138, -1687644479, -1645515069, -1617635994, -1610444000, -1579053372, -1556891649, -1549652116, -1537732956, -1535180388, -1527162056, -1524851611, -1524658412, -1523244369, -1521379172, -1520191198, -1519035741, -1516978241, -1508892332, -1489938422, -1482102944, -1481823232, -1470621147, -1469145091, -1446844485, -1441790509, -1437843276, -1435359182, -1434186947, -1429816311, -1429393781, -1419752032, -1400387846, -1385152926, -1372620863, -1369257355, -1361933674, -1360480816, -1334846204, -1323741718, -1323660173, -1312800992, -1308824840, -1304658551, -1287829999, -1283767920, -1276288210, -1264275838, -1263965596, -1262866901, -1255421887, -1251428680, -1244825786, -1243200329, -1235305532, -1233977691, -1220537074, -1214100716, -1199414474, -1190725823, -1190401800, -1178717689, -1172378149, -1147869245, -1142875190, -1138538768, -1137864183, -1124917489, -1102987222, -1095920186, -1083001017, -1080902655, -1047122002, -1031842676, -1029877334, -1020849489, -1001684838, -998419619, -990915088, -985235989, -982515261, -979074894, -974195629, -973832940, -965324937, -944246431, -938387588, -933873331, -932692878, -928039285, -927947459, -914008773, -907981688, -906376330, -903502449, -898112547, -887444438, -862658502, -843628573, -822463032, -786051095, -776932426, -776033951, -752042328, -746532472, -743149468, -740225710, -734414418, -725435852, -708101516, -699674783, -694869277, -693246525, -690571518, -689249770, -688581912, -686864294, -681445866, -647992869, -641101583, -631409299, -624686189, -613079884, -593711206, -591688546, -591331185, -574790069, -573024823, -565387051, -565137163, -556338668, -556291492, -541411509, -538932064, -500479857, -482419890, -468050561, -424532545, -420534171, -408741873, -406973874, -387664799, -382084509, -367095703, -352332569, -352195997, -346430007, -324596389, -320119776, -306594578, -305952425, -283718911, -267302378, -243302738, -242955859, -232180029, -225394407, -217418127, -212286453, -208344820, -191300139, -186177744, -175765723, -161763935, -157025501, -140389149, -132298608, -126175769, -70566352, -68748576, -53985905, -52674668, -50228620, -39678495, -19825663, -8349922, -8186722, -8125700, -8073135, -8043230, -7994382, -7874433, -7863624, -7784916, -7782477, -7696343, -7607278, -7531250, -7388060, -7368780, -7367625, -7353084, -7334489, -7281141, -7267149, -7140057, -7119066, -7010389, -6992089, -6975258, -6863360, -6784772, -6741079, -6585985, -6550401, -6520011, -6495144, -6459702, -6294273, -6178342, -6169344, -6139663, -6090928, -6022637, -5992707, -5971334, -5925304, -5880940, -5873707, -5807953, -5703992, -5692895, -5535131, -5488812, -5468330, -5404148, -5290247, -5274221, -5264144, -5234715, -5224048, -5179837, -5084014, -5043990, -5028537, -5011679, -4998333, -4922901, -4880159, -4874060, -4787390, -4749096, -4736217, -4502308, -4480611, -4424319, -4363262, -4349743, -4290050, -4240069, -4239657, -4174072, -4093051, -4045363, -4037689, -4033352, -3839265, -3766343, -3716899, -3680075, -3679053, -3581776, -3539227, -3461158, -3282526, -3205947, -3183427, -3169708, -3166430, -3089822, -3061531, -2947574, -2930733, -2919246, -2872882, -2830770, -2739228, -2713826, -2634018, -2613990, -2525529, -2439507, -2432921, -2376201, -2335005, -2307524, -2265548, -2176176, -2123133, -2108773, -2105934, -2075032, -2073940, -2045837, -2045648, -1978182, -1945769, -1935486, -1881608, -1654650, -1602520, -1506746, -1505294, -1475309, -1457605, -1327259, -1312217, -1178723, -1027439, -880781, -833776, -666675, -643098, -593446, -468772, -450369, -443225, -418164, -402004, -319964, -307400, -279414, -190199, -176644, -66862, -32745, -32686, -32352, -32261, -32035, -31928, -31414, -31308, -30925, -30411, -29503, -29182, -28573, -28500, -28093, -27743, -27716, -27351, -27201, -26834, -25946, -25019, -24469, -24341, -24292, -24151, -23732, -22769, -22242, -22002, -20863, -20762, -20644, -20189, -20009, -19142, -19036, -18980, -18616, -18196, -18123, -17942, -17915, -17601, -17494, -16669, -16417, -16317, -15051, -14796, -14742, -14600, -14443, -14159, -14046, -13860, -13804, -13745, -13634, -13498, -13497, -12688, -12471, -12222, -11993, -11467, -11332, -10783, -10250, -10114, -10089, -9930, -9434, -9336, -9128, -9109, -8508, -8460, -8198, -8045, -7850, -7342, -7229, -6762, -6302, -6245, -6171, -5957, -5842, -4906, -4904, -4630, -4613, -4567, -4427, -4091, -4084, -3756, -3665, -3367, -3186, -2922, -2372, -2331, -1936, -1683, -1350, -1002, -719, -152, -128, -127, -124, -122, -121, -119, -116, -113, -112, -111, -107, -104, -102, -101, -100, -95, -94, -91, -90, -87, -81, -80, -79, -78, -73, -72, -69, -68, -66, -65, -63, -57, -54, -52, -51, -48, -47, -46, -45, -43, -41, -37, -33, -31, -30, -27, -25, -21, -18, -15, -12, -8, -1, 0, 1, 3, 4, 5, 6, 11, 14, 17, 23, 25, 26, 27, 28, 29, 31, 32, 39, 41, 46, 49, 51, 52, 56, 58, 61, 64, 66, 67, 70, 74, 79, 80, 86, 88, 89, 92, 93, 99, 102, 104, 109, 113, 117, 120, 122, 123, 127, 695, 912, 1792, 2857, 3150, 3184, 4060, 4626, 5671, 6412, 6827, 7999, 8017, 8646, 8798, 9703, 9837, 10049, 10442, 10912, 11400, 11430, 11436, 11551, 11937, 12480, 13258, 13469, 13689, 13963, 13982, 14019, 14152, 14259, 14346, 15416, 15613, 15954, 16241, 16814, 16844, 17564, 17702, 17751, 18537, 18763, 19890, 21216, 22238, 22548, 23243, 23383, 23386, 23407, 23940, 24076, 24796, 24870, 24898, 24967, 25139, 25176, 25699, 26167, 26536, 26614, 27008, 27087, 27142, 27356, 27458, 27800, 27827, 27924, 28595, 29053, 29229, 29884, 29900, 30460, 30556, 30701, 30815, 30995, 31613, 31761, 31772, 32099, 32308, 32674, 75627, 80472, 103073, 110477, 115718, 172418, 212268, 242652, 396135, 442591, 467087, 496849, 675960, 759343, 846297, 881562, 1003458, 1153900, 1156733, 1164679, 1208265, 1318372, 1363958, 1411655, 1522329, 1559609, 1677118, 1693658, 1703597, 1811223, 1831642, 1838628, 1884144, 1931545, 2085504, 2168156, 2170263, 2239585, 2308894, 2329235, 2364957, 2432335, 2435551, 2596936, 2684907, 2691011, 2705195, 2738057, 2851897, 2925289, 2995414, 3051534, 3216094, 3267022, 3271559, 3338856, 3440797, 3638325, 3651369, 3718696, 3724814, 3811069, 3854697, 3866969, 3893228, 3963455, 3984546, 4098376, 4100957, 4128113, 4200719, 4256344, 4286332, 4306356, 4316314, 4438803, 4458063, 4461638, 4552228, 4563790, 4584831, 4607992, 4884455, 4907501, 5045419, 5066844, 5150624, 5157161, 5190669, 5314703, 5337397, 5434807, 5440092, 5502665, 5523089, 5547122, 5566200, 5582936, 5634068, 5690330, 5776984, 5778441, 5818505, 5826687, 5827184, 5885735, 6010506, 6084254, 6131498, 6138324, 6250773, 6292801, 6306275, 6315242, 6331640, 6484374, 6502969, 6545970, 6666951, 6690905, 6763576, 6766086, 6895048, 6912227, 6929081, 6941390, 6978168, 7045672, 7085246, 7193307, 7197398, 7270237, 7276767, 7295790, 7375488, 7472098, 7687424, 7840758, 7880957, 7904499, 7948678, 7974126, 8015691, 8037685, 8112955, 8131380, 8140556, 8142384, 8220436, 8308817, 8331317, 22581970, 45809129, 48103779, 78212045, 79674901, 97299830, 110308649, 131744428, 136663461, 138485719, 139842794, 152061792, 152685704, 153070991, 156228213, 164884737, 174776199, 189346581, 193148547, 208582124, 223891881, 227308187, 237373798, 241214067, 242476929, 245495851, 260606593, 275202667, 285717038, 317009689, 322759532, 325369206, 339724742, 340122632, 345010859, 352375176, 355826263, 359695034, 366118516, 370008270, 382712922, 386379440, 401153345, 404986391, 426084981, 442843409, 473909474, 475192613, 492302667, 494747879, 506279889, 509813998, 537558350, 548423414, 548467404, 566383324, 574188786, 574792333, 591678147, 596558084, 597423476, 602432742, 603067874, 629552047, 630893263, 635249783, 644959276, 650710927, 664859367, 669433203, 684329599, 699991513, 714451929, 723556530, 739294558, 750895264, 757618344, 781123405, 796973385, 801637715, 804776709, 829003666, 829219068, 840167037, 854882202, 860066192, 864304878, 864808449, 867107161, 871871263, 880591851, 883020336, 883178082, 920223781, 936008673, 939417822, 956776353, 958281059, 962183717, 964059257, 967860573, 974322643, 974999286, 980009921, 1032949015, 1044249483, 1064892676, 1075628270, 1080848022, 1085571657, 1173635593, 1174809080, 1176744978, 1209783795, 1212074975, 1252323507, 1254757790, 1301450562, 1302240953, 1314501797, 1315121266, 1339304157, 1364304289, 1376260506, 1383883477, 1395158643, 1411117754, 1440755058, 1448365702, 1466814914, 1468433821, 1490105126, 1493912601, 1495600372, 1509536621, 1511014977, 1545693948, 1548924199, 1566583103, 1569747154, 1574097219, 1597784674, 1610710480, 1618324005, 1646105187, 1649417465, 1655649169, 1660619384, 1668826887, 1671093718, 1672456990, 1673477565, 1678638502, 1682302139, 1682515769, 1687920300, 1690062315, 1706031388, 1713660819, 1772170709, 1778416812, 1833443690, 1861312062, 1876004501, 1876358085, 1882435551, 1916050713, 1944906037, 1950207172, 1951593247, 1973638546, 1976288281, 1994977271, 2020053060, 2025281195, 2029716419, 2033980539, 2052482076, 2058251762, 2069273004, 2073978021, 2111013213, 2119886932, 2134609957, 2140349794, 2143934987]:
print(i,best_or_l(i,True),len(l(i)),len(best_or_l(i,True)))
score = score + (len(l(i))-len(best_or_l(i,True)))
print("Score:",score)

with open("brute_serious.json","w") as outfile:
outfile.write(json.dumps(best,sort_keys=True,indent=2))

Here's a random sampling of the sorts of Actually programs that end up found by this algorithm:

-387420483 99ⁿ6-
-16777208 4!╙8-
-999999 6╤1-
-362864 9!4²-
-46369 4!Fu±
-5045 57!±-
8101 9eL¬
19900 2╤τrΣ
46367 4!FD
68072 5╙│F\
99990 1╤5╤-
156246 75ⁿ¬τ
518393 76!²-
1814399 59!*D
6534927 35╙F*
14930357 56²F+
19999995 57╤τ-
25396560 7!│D*
65691025 9eKu²
100001000 3╤8╤+
200000002 8╤uτ
800000008 88╤u*
1626347584 88!+²
2000000018 99╤+τ

# Ruby, 52 chars saved

based off my answer to a similar question. This builds up a big list of ways to get to a number and selects the shortest. Unlike the other answers posted, It gets most of its savings on small numbers. In fact i do not try numbers with absolute values over 2000.

$s = {}; Fact = [1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880] Fib = [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, 832040, 1346269, 2178309, 3524578, 5702887, 9227465, 14930352, 24157817, 39088169, 63245986, 102334155, 165580141, 267914296, 433494437, 701408733, 1134903170, 1836311903] Prime = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999] def shortest a,b=nil return$s[[a,b]] if $s[[a,b]] return$s[[a,b]] = ":#{a}" if (b||a).abs > 2000 #gives up on big inputs
$s[[a,b]] = ":#{a}" #set a temp value to block calling with the same paramiters recursivly. l = [] if b if a == b return$s[[a,b]] = ""
elsif a > b
l.push shortest(a-b)+"-"
l.push "X"+shortest(b)
l.push "¬" if b+2==a
l.push "D" if b+1==a
elsif a < b
l.push shortest(b-a)+"+"
l.push "²"+shortest(a*a,b) if a*a>a && a*a<=b+2
l.push "τ"+shortest(a+a,b) if a+a<=b+2 && a+a>a
l.push shortest(b/a)+"*" if a>2 && b%a == 0
l.push ";"+shortest(a,b/a)+"*" if a>2 && b%a == 0
l.push "╙"+shortest(2**a,b) if 2**a<=b+2
l.push "╤"+shortest(10**a,b) if 10**a<=b+2
l.push "F"+shortest(Fib[a],b) if Fib[a] and Fib[a]<=b+2 and a > 5
l.push "P"+shortest(Prime[a],b) if Prime[a] and Prime[a]<=b+2
l.push "!"+shortest(Fact[a],b) if Fact[a] and Fact[a]<=b+2 and a > 3
end
else
return ($s[[a,b]] = a.to_s) if a<10 and a>-1 l.push ":#{a}" if a<0 l.push shortest(-a)+"±" l.push shortest(~a)+"~" l.push shortest(a+1)+"D" l.push shortest(a+2)+"¬" else l.push shortest(a-1)+"u" l.push shortest(a-2)+"⌐" (1..[a/2,100].min).each {|n| l.push shortest(n)+shortest(n,a) } end end return$s[[a,b]] = l.min_by{|x|x.length}
end

a = [-4427,-4091,-4084,-3756,-3665,-3367,-3186,-2922,-2372,-2331,-1936,-1683,-1350,-1002,-719,-152,-128,-127,-124,-122,-121,-119,-116,-113,-112,-111,-107,-104,-102,-101,-100,-95,-94,-91,-90,-87,-81,-80,-79,-78,-73,-72,-69,-68,-66,-65,-63,-57,-54,-52,-51,-48,-47,-46,-45,-43,-41,-37,-33,-31,-30,-27,-25,-21,-18,-15,-12,-8,-1,0,1,3,4,5,6,11,14,17,23,25,26,27,28,29,31,32,39,41,46,49,51,52,56,58,61,64,66,67,70,74,79,80,86,88,89,92,93,99,102,104,109,113,117,120,122,123,127,695,912,1792,2857,3150,3184,4060,4626,5671,6412,6827,7999,8017]
a.sort_by!{|x|x.abs}
c = a.map{
|i|
p [i,shortest(i)]
shortest(i)
}
p c.inject(0){|a,b|a+b.length}

And a complete list of all shortened numbers (sorted by absolute value):

[0, "0"]
[-1, "1±"]
[1, "1"]
[3, "3"]
[4, "4"]
[5, "5"]
[6, "6"]
[-8, "8±"]
[11, "9⌐"]
[-12, "6τ±"]
[14, "7τ"]
[-15, "7τ~"]
[17, "6P"]
[-18, "9τ±"]
[-21, "8F±"]
[23, "8P"]
[25, "5²"]
[-25, "5²±"]
[29, "9P"]
[-30, "9P~"]
[32, "5╙"]
[-33, "5╙~"]
[-37, "6²~"]
[49, "7²"]
[64, "6╙"]
[-65, "6╙~"]
[-81, "9²±"]
[-100, "2╤±"]
[-101, "2╤~"]
[-102, "2╤⌐±"]
[102, "2╤⌐"]
[113, "9PP"]
[-113, "9PP±"]
[-119, "5!D±"]
[120, "5!"]
[-121, "5!~"]
[122, "5!⌐"]
[-122, "5!⌐±"]
[127, "7╙D"]
[-127, "7╙D±"]
[-128, "7╙±"]
[-719, "6!D±"]
[-1002, "3╤⌐±"]
[-1683, "9P²τ~"]
[1792, "78╙*"]
[-1936, ":44²±"]

Note: These have not bean tested as I do not have access to Actually.

• I quickly noticed you're using ~ and I'm not, which saves a couple of bytes. I spent 30 minutes figuring out why your score for the small numbers was better when I find a handful that you don't. I finally realized I was counting the trivial case for 0-9 as 0-9, not :0-:9. Cost myself 6 points on all three solutions. Thanks for making me investigate that. – Sparr May 20 '16 at 5:46
• @sparr I had a feeling that this would only help you do better. – MegaTom May 20 '16 at 10:50

## Python 3, 52 55 bytes saved

This solution works backwards from the previous two. Instead of assembling programs left to right, I start at the end and work backwards. To make this work, I've got to actually run my programs, and I can't prune instructions based on their parameters because their parameters don't exist yet when they get added. My workaround for that is not present in this answer; it involves telling SeriouslyCommands.py to throw an IOError any time the craziness-producing functions get called with large arguments, and to raise that exception so I can catch it.

Here's how this program works:

I start with an empty stack and know I want a single number. What instructions can accomplish that? 0-9 get me an integer and don't require anything on the stack, so those are complete programs. K,L,T,e and a bunch of others get me a number and need a number (I don't differentiate between floats and ints until the output is checked). *,+,etc turn two numbers into a number. And so on.

Now I have a few complete programs and a list of incomplete program-suffixes that can turn some known arrangement of types on the stack into the single number I want. Repeat the process and prepend to each them every instruction that can fulfill one/some/all of their stack requirements, save the ones that are complete programs, and send the incomplete ones to the next step.

In the last two steps I prune the possibilities a lot because I know I can't have any stack requirements left when I'm done (so 0-9 are the only valid instructions to be prepended to the program last) and prior to that I can only have a single number as a requirement.

Not surprisingly, this solution produces exactly the same score as the better of my other two solutions. They find almost exactly the same set of results.

This program can probably go up to 6 characters in less time than the other one, but it would still be prohibitive.

I think a great solution could be made by combining the two, assembling prefixes and suffixes and joining them in the middle if their stacks are compatible.

#!/usr/bin/env python3
# -*- coding: cp437 -*-

import os
import sys
import json
import math
import time
import random
import timeit

#!/usr/bin/env python3
# -*- coding: cp437 -*-

# instruction, pops, pushes,
instructions = [
[0x30, [], ['number']], #  (0): push 0
[0x31, [], ['number']], #  (1): push 1
[0x32, [], ['number']], #  (2): push 2
[0x33, [], ['number']], #  (3): push 3
[0x34, [], ['number']], #  (4): push 4
[0x35, [], ['number']], #  (5): push 5
[0x36, [], ['number']], #  (6): push 6
[0x37, [], ['number']], #  (7): push 7
[0x38, [], ['number']], #  (8): push 8
[0x39, [], ['number']], #  (9): push 9

[0x4B, ['number'], ['number']], #  (K): pop a: push ceil(a)
[0x4C, ['number'], ['number']], #  (L): pop a: push floor(a)

[0x54, ['number'], ['number']], #  (T): pop a: push tan(a); pop [a],b,c: set [a][b] to c, push [a]
[0x65, ['number'], ['number']], #  (e): pop a: push exp(a)

[0xAB, ['number'], ['number']], #  (½): pop a: push a/2 (float division)
[0xAC, ['number'], ['number']], #  (¼): pop a: push a/4 (float division)

[0x21, ['number'], ['number']], #  (!): pop a: push a! (factorial(a))
[0x44, ['number'], ['number']], #  (D): pop a: push a-1; pop [a]: push stddev([a])
[0x46, ['number'], ['number']], #  (F): pop a: push Fib(a) (Fib(0)=0, Fib(1)=Fib(2)=1); pop [a]: push a[0]
[0x50, ['number'], ['number']], #  (P): pop a: push the a-th prime (zero-indexed)
[0x75, ['number'], ['number']], #  (u): pop a: push a+1
[0x7E, ['number'], ['number']], #  (~): pop a: push ~a (unary bitwise negate)
[0xA9, ['number'], ['number']], #  (⌐): pop a: push a+2
[0xAA, ['number'], ['number']], #  (¬): pop a: push a-2
[0xD1, ['number'], ['number']], #  (╤): pop a: push 10**a
[0xD3, ['number'], ['number']], #  (╙): pop a: push 2**a
[0xE7, ['number'], ['number']], #  (τ): pop a: push 2*a
[0xF1, ['number'], ['number']], #  (±): pop a: push -a (unary negate)
[0xFD, ['number'], ['number']], #  (²): pop a: push a*a

[0x2A, ['number','number'], ['number']], #  (*): pop a,b: push a*b; pop a,[b] or [b],a: apply a* to each element in the array; pop [a],[b]: push dot product of [a] and [b] (sum([a[i]*b[i] for i in len(a)]) (shorter is padded with 0s)
[0x2B, ['number','number'], ['number']], #  (+): pop a,b: push a+b; pop [a],[b]: push [a][b] (append [b] to [a]); pop a,[b] or [b],a: apply a+ to each element in the array
[0x2D, ['number','number'], ['number']], #  (-): pop a,b: push a-b; pop [a],[b]: push [a]-[b] (all elements of [a] not in [b])
[0x2F, ['number','number'], ['number']], #  (/): pop a,b: push a/b (float division); pop [a]: rotate [a] right by 1, push [a]
[0x5C, ['number','number'], ['number']], #  (\): pop a,b: push a/b (integer division); pop [a]: rotate [a] left by 1, push [a]
[0xFC, ['number','number'], ['number']], #  (ⁿ): pop a,b: push pow(a,b)

[0xDB, ['number','number'], ['number']], #  (█): pop a,b: push C(a,b) (aCb)
[0xDC, ['number','number'], ['number']], #  (▄): pop a,b: push P(a,b) (aPb)

[0x3B, ['number'], ['number','number']], #  (;): pop a: push a,a (duplicates top element)

[0xE3, ['list'], ['number']], #  (π): pop [a]: push product([a])
[0xE4, ['list'], ['number']], #  (Σ): pop [a]: push sum([a])

[0x69, ['list'], ['numbers']], #  (i): pop [a]: push each element from [a], starting from end (flatten)

[0xC6, ['numbers'], ['numbers']], #  (╞): pop a: make a total copies of each element on stack (3 [a,b,c] -> [a,a,a,b,b,b,c,c,c])

[0xC7, ['numbers'], ['list']], #  (╟): pop a: pop a elements and push a list containing those elements in their original order

[0x0B, ['list'], ['list']], #  (♂): take the next command and map it over the top of the stack (for example, ♂A is equivalent to AM)

[0x61, ['numbers'], ['numbers']], #  (a): invert the stack ([a,b,c,d] -> [d,c,b,a])
[0xB3, ['numbers'], ['numbers']], #  (│): duplicate stack ([a,b,c] => [a,b,c,a,b,c])
[0xC5, ['numbers'], ['numbers']], #  (┼): duplicate each element on stack ([a,b,c] => [a,a,b,b,c,c])

[0x72, ['number'], ['list']], #  (r): pop a: push [0,1,...,a-1] (range(0,a))
[0xB9, ['number'], ['list']], #  (╣): pop a: push the ath row in Pascal's triangle

[0x78, ['number','number'], ['list']], #  (x): pop a,b: push [a,b) (range(a,b)); pop [a]: push range(*a)
[0x78, ['list'], ['list']], #  (x): pop a,b: push [a,b) (range(a,b)); pop [a]: push range(*a)

[0x6B, ['numbers'], ['list']],#  (k): pop all elements from stack, convert to list (in the order they were on the stack, starting from the top) and push

# 0x3A, #  (:): numeric literal delimiter: pushes the longest string of characters in '0123456789+-.ij' as a numeric
# 0x4D, #  (M): pop f,[a], execute f for each element in [a], using the element as a temporary stack, push [a] (similar to map(f,[a])); pop [a]: push max([a])
# 0x52, #  (R): pop f,[a]: call f, using [a] as a temporary stack, push [a] (similar to reduce(f,[a])); pop [a]: push [a][::-1] (reverse); pop a: push [1,2,...,a] (range(1,a+1))
# 0x57, #  (W): loop delimiter: peek top of stack, repeat code in loop while a evaluates to true
# 0x60, #  (): function literal delimiter, pushes function whose body contains all of the commands until the next . An implied ` is present at EOF if needed.
]

provides = {
'number':[],
'numbers':[],
'list':[]
}

wants = [[]]*256

for i in instructions:
wants[i[0]] = i[1]
provides[i[2][0]].append(i[0])

from seriously import Seriously,chr_cp437,ord_cp437

MAX=2**31

# returns ([finished programs],[new programs]), one of which will be empty
def extend_program(p):
finished_programs=[]
new_programs=[]
# print(p)
for i in provides[p[1][-1]]:
new_p = chr_cp437(i)+p[0]
new_wants = p[1][:-1]+wants[i]
if new_wants==[]: # we've reached a complete program! run it
# print(p[0])
now = time.clock()
# print(p[0])
try:
res = Seriously().eval(new_p)
except:
return ([],[])
# print(res)
elapsed = time.clock()-now
if elapsed>0.001:
try:
elapsed = timeit.timeit('Seriously().eval("'+str(new_p.encode('unicode_escape'))+'")','from seriously import Seriously',number=1000)
except:
continue
if elapsed>0.005:
print("SLOW:")
print(new_p)
print(res)
print(elapsed)
# print(res)
finished_programs.append([new_p,res])
continue
if len(new_p)==MAXLEN and new_wants!=[]: # no room left to fulfill any wants
continue
if len(new_p)==MAXLEN-1 and new_wants != ['number']: # no room left to fulfill complex wants
continue
new_programs.append([new_p,new_wants])
if len(p[1])>1 and p[1][-1]=='number' and p[1][-2]=='number':
for i in provides['numbers']:
new_p = chr_cp437(i)+p[0]
old_wants = p[1]
while len(p[1]) and p[1][-1]=='number':
p[1].pop()
new_wants = old_wants+wants[i]
if len(new_p)==MAXLEN and new_wants!=[]:
continue
if len(new_p)==MAXLEN-1 and \
new_wants != ['list'] and \
new_wants != ['number'] and \
new_wants != ['numbers']:
continue
new_programs.append([new_p,new_wants])
return (finished_programs,new_programs)

unfinished_programs = [['',['number']]]
best = {}

def l(n,force_colon=False):
if force_colon:
return ':'+str(n)
if n>=0 and n<10:
return str(n)
elif n<0 and n>-10:
return str(-n)+'±'
return ':'+str(n)

def cand(n,rep):
# print(n,rep,len(rep),l(n),len(l(n)),best[n] if n in best else "")
if n<=MAX and n>=-MAX and (len(rep)==1 or len(rep)<len(l(n))) and (n not in best or len(rep)<len(best[n])):
best[n] = rep
# print("woot")
return True
return False

MAXLEN = 5

for i in range(MAXLEN):
print(i+1,"/",MAXLEN)
new_unfinished_programs = []
c = ''
for p in unfinished_programs:
if len(p[0]) and p[0][-1]!= c:
print(c)
c=p[0][-1]
(finished_programs,new_programs) = extend_program(p)
for f in finished_programs:
# print(f[0])
# print(f[1][0])
if len(f[1])==0:
# print("TOO MANY RESULTS")
continue
if isinstance(f[1][0],int):
cand(f[1][0],f[0])
# if isinstance(f[1][0],list):
# print("LIST RESULT")
new_unfinished_programs = new_unfinished_programs + new_programs
unfinished_programs = new_unfinished_programs

def best_or_l(n,force_colon=False):
if n in best:
return best[n]
if n<0 and -n in best:
return best[-n]+"±"
return l(n,force_colon)

for key,value in sorted(best.items()):
# if random.random()<0.01:
print(key,value)

score = 0
for i in [-2124910654, -2117700574, -2098186988, -2095671996, -2083075613, -2058271687, -2052250777, -2024215903, -2019485642, -2016095616, -2009838326, -2009173317, -2007673992, -2000014444, -1999825668, -1992515610, -1989566707, -1975506037, -1955473208, -1950731112, -1949886423, -1920624450, -1918465596, -1916287469, -1905036556, -1903956118, -1888944417, -1865221863, -1856600057, -1842797147, -1835637734, -1812631357, -1805740096, -1798015647, -1726688233, -1723609647, -1713776890, -1700307138, -1687644479, -1645515069, -1617635994, -1610444000, -1579053372, -1556891649, -1549652116, -1537732956, -1535180388, -1527162056, -1524851611, -1524658412, -1523244369, -1521379172, -1520191198, -1519035741, -1516978241, -1508892332, -1489938422, -1482102944, -1481823232, -1470621147, -1469145091, -1446844485, -1441790509, -1437843276, -1435359182, -1434186947, -1429816311, -1429393781, -1419752032, -1400387846, -1385152926, -1372620863, -1369257355, -1361933674, -1360480816, -1334846204, -1323741718, -1323660173, -1312800992, -1308824840, -1304658551, -1287829999, -1283767920, -1276288210, -1264275838, -1263965596, -1262866901, -1255421887, -1251428680, -1244825786, -1243200329, -1235305532, -1233977691, -1220537074, -1214100716, -1199414474, -1190725823, -1190401800, -1178717689, -1172378149, -1147869245, -1142875190, -1138538768, -1137864183, -1124917489, -1102987222, -1095920186, -1083001017, -1080902655, -1047122002, -1031842676, -1029877334, -1020849489, -1001684838, -998419619, -990915088, -985235989, -982515261, -979074894, -974195629, -973832940, -965324937, -944246431, -938387588, -933873331, -932692878, -928039285, -927947459, -914008773, -907981688, -906376330, -903502449, -898112547, -887444438, -862658502, -843628573, -822463032, -786051095, -776932426, -776033951, -752042328, -746532472, -743149468, -740225710, -734414418, -725435852, -708101516, -699674783, -694869277, -693246525, -690571518, -689249770, -688581912, -686864294, -681445866, -647992869, -641101583, -631409299, -624686189, -613079884, -593711206, -591688546, -591331185, -574790069, -573024823, -565387051, -565137163, -556338668, -556291492, -541411509, -538932064, -500479857, -482419890, -468050561, -424532545, -420534171, -408741873, -406973874, -387664799, -382084509, -367095703, -352332569, -352195997, -346430007, -324596389, -320119776, -306594578, -305952425, -283718911, -267302378, -243302738, -242955859, -232180029, -225394407, -217418127, -212286453, -208344820, -191300139, -186177744, -175765723, -161763935, -157025501, -140389149, -132298608, -126175769, -70566352, -68748576, -53985905, -52674668, -50228620, -39678495, -19825663, -8349922, -8186722, -8125700, -8073135, -8043230, -7994382, -7874433, -7863624, -7784916, -7782477, -7696343, -7607278, -7531250, -7388060, -7368780, -7367625, -7353084, -7334489, -7281141, -7267149, -7140057, -7119066, -7010389, -6992089, -6975258, -6863360, -6784772, -6741079, -6585985, -6550401, -6520011, -6495144, -6459702, -6294273, -6178342, -6169344, -6139663, -6090928, -6022637, -5992707, -5971334, -5925304, -5880940, -5873707, -5807953, -5703992, -5692895, -5535131, -5488812, -5468330, -5404148, -5290247, -5274221, -5264144, -5234715, -5224048, -5179837, -5084014, -5043990, -5028537, -5011679, -4998333, -4922901, -4880159, -4874060, -4787390, -4749096, -4736217, -4502308, -4480611, -4424319, -4363262, -4349743, -4290050, -4240069, -4239657, -4174072, -4093051, -4045363, -4037689, -4033352, -3839265, -3766343, -3716899, -3680075, -3679053, -3581776, -3539227, -3461158, -3282526, -3205947, -3183427, -3169708, -3166430, -3089822, -3061531, -2947574, -2930733, -2919246, -2872882, -2830770, -2739228, -2713826, -2634018, -2613990, -2525529, -2439507, -2432921, -2376201, -2335005, -2307524, -2265548, -2176176, -2123133, -2108773, -2105934, -2075032, -2073940, -2045837, -2045648, -1978182, -1945769, -1935486, -1881608, -1654650, -1602520, -1506746, -1505294, -1475309, -1457605, -1327259, -1312217, -1178723, -1027439, -880781, -833776, -666675, -643098, -593446, -468772, -450369, -443225, -418164, -402004, -319964, -307400, -279414, -190199, -176644, -66862, -32745, -32686, -32352, -32261, -32035, -31928, -31414, -31308, -30925, -30411, -29503, -29182, -28573, -28500, -28093, -27743, -27716, -27351, -27201, -26834, -25946, -25019, -24469, -24341, -24292, -24151, -23732, -22769, -22242, -22002, -20863, -20762, -20644, -20189, -20009, -19142, -19036, -18980, -18616, -18196, -18123, -17942, -17915, -17601, -17494, -16669, -16417, -16317, -15051, -14796, -14742, -14600, -14443, -14159, -14046, -13860, -13804, -13745, -13634, -13498, -13497, -12688, -12471, -12222, -11993, -11467, -11332, -10783, -10250, -10114, -10089, -9930, -9434, -9336, -9128, -9109, -8508, -8460, -8198, -8045, -7850, -7342, -7229, -6762, -6302, -6245, -6171, -5957, -5842, -4906, -4904, -4630, -4613, -4567, -4427, -4091, -4084, -3756, -3665, -3367, -3186, -2922, -2372, -2331, -1936, -1683, -1350, -1002, -719, -152, -128, -127, -124, -122, -121, -119, -116, -113, -112, -111, -107, -104, -102, -101, -100, -95, -94, -91, -90, -87, -81, -80, -79, -78, -73, -72, -69, -68, -66, -65, -63, -57, -54, -52, -51, -48, -47, -46, -45, -43, -41, -37, -33, -31, -30, -27, -25, -21, -18, -15, -12, -8, -1, 0, 1, 3, 4, 5, 6, 11, 14, 17, 23, 25, 26, 27, 28, 29, 31, 32, 39, 41, 46, 49, 51, 52, 56, 58, 61, 64, 66, 67, 70, 74, 79, 80, 86, 88, 89, 92, 93, 99, 102, 104, 109, 113, 117, 120, 122, 123, 127, 695, 912, 1792, 2857, 3150, 3184, 4060, 4626, 5671, 6412, 6827, 7999, 8017, 8646, 8798, 9703, 9837, 10049, 10442, 10912, 11400, 11430, 11436, 11551, 11937, 12480, 13258, 13469, 13689, 13963, 13982, 14019, 14152, 14259, 14346, 15416, 15613, 15954, 16241, 16814, 16844, 17564, 17702, 17751, 18537, 18763, 19890, 21216, 22238, 22548, 23243, 23383, 23386, 23407, 23940, 24076, 24796, 24870, 24898, 24967, 25139, 25176, 25699, 26167, 26536, 26614, 27008, 27087, 27142, 27356, 27458, 27800, 27827, 27924, 28595, 29053, 29229, 29884, 29900, 30460, 30556, 30701, 30815, 30995, 31613, 31761, 31772, 32099, 32308, 32674, 75627, 80472, 103073, 110477, 115718, 172418, 212268, 242652, 396135, 442591, 467087, 496849, 675960, 759343, 846297, 881562, 1003458, 1153900, 1156733, 1164679, 1208265, 1318372, 1363958, 1411655, 1522329, 1559609, 1677118, 1693658, 1703597, 1811223, 1831642, 1838628, 1884144, 1931545, 2085504, 2168156, 2170263, 2239585, 2308894, 2329235, 2364957, 2432335, 2435551, 2596936, 2684907, 2691011, 2705195, 2738057, 2851897, 2925289, 2995414, 3051534, 3216094, 3267022, 3271559, 3338856, 3440797, 3638325, 3651369, 3718696, 3724814, 3811069, 3854697, 3866969, 3893228, 3963455, 3984546, 4098376, 4100957, 4128113, 4200719, 4256344, 4286332, 4306356, 4316314, 4438803, 4458063, 4461638, 4552228, 4563790, 4584831, 4607992, 4884455, 4907501, 5045419, 5066844, 5150624, 5157161, 5190669, 5314703, 5337397, 5434807, 5440092, 5502665, 5523089, 5547122, 5566200, 5582936, 5634068, 5690330, 5776984, 5778441, 5818505, 5826687, 5827184, 5885735, 6010506, 6084254, 6131498, 6138324, 6250773, 6292801, 6306275, 6315242, 6331640, 6484374, 6502969, 6545970, 6666951, 6690905, 6763576, 6766086, 6895048, 6912227, 6929081, 6941390, 6978168, 7045672, 7085246, 7193307, 7197398, 7270237, 7276767, 7295790, 7375488, 7472098, 7687424, 7840758, 7880957, 7904499, 7948678, 7974126, 8015691, 8037685, 8112955, 8131380, 8140556, 8142384, 8220436, 8308817, 8331317, 22581970, 45809129, 48103779, 78212045, 79674901, 97299830, 110308649, 131744428, 136663461, 138485719, 139842794, 152061792, 152685704, 153070991, 156228213, 164884737, 174776199, 189346581, 193148547, 208582124, 223891881, 227308187, 237373798, 241214067, 242476929, 245495851, 260606593, 275202667, 285717038, 317009689, 322759532, 325369206, 339724742, 340122632, 345010859, 352375176, 355826263, 359695034, 366118516, 370008270, 382712922, 386379440, 401153345, 404986391, 426084981, 442843409, 473909474, 475192613, 492302667, 494747879, 506279889, 509813998, 537558350, 548423414, 548467404, 566383324, 574188786, 574792333, 591678147, 596558084, 597423476, 602432742, 603067874, 629552047, 630893263, 635249783, 644959276, 650710927, 664859367, 669433203, 684329599, 699991513, 714451929, 723556530, 739294558, 750895264, 757618344, 781123405, 796973385, 801637715, 804776709, 829003666, 829219068, 840167037, 854882202, 860066192, 864304878, 864808449, 867107161, 871871263, 880591851, 883020336, 883178082, 920223781, 936008673, 939417822, 956776353, 958281059, 962183717, 964059257, 967860573, 974322643, 974999286, 980009921, 1032949015, 1044249483, 1064892676, 1075628270, 1080848022, 1085571657, 1173635593, 1174809080, 1176744978, 1209783795, 1212074975, 1252323507, 1254757790, 1301450562, 1302240953, 1314501797, 1315121266, 1339304157, 1364304289, 1376260506, 1383883477, 1395158643, 1411117754, 1440755058, 1448365702, 1466814914, 1468433821, 1490105126, 1493912601, 1495600372, 1509536621, 1511014977, 1545693948, 1548924199, 1566583103, 1569747154, 1574097219, 1597784674, 1610710480, 1618324005, 1646105187, 1649417465, 1655649169, 1660619384, 1668826887, 1671093718, 1672456990, 1673477565, 1678638502, 1682302139, 1682515769, 1687920300, 1690062315, 1706031388, 1713660819, 1772170709, 1778416812, 1833443690, 1861312062, 1876004501, 1876358085, 1882435551, 1916050713, 1944906037, 1950207172, 1951593247, 1973638546, 1976288281, 1994977271, 2020053060, 2025281195, 2029716419, 2033980539, 2052482076, 2058251762, 2069273004, 2073978021, 2111013213, 2119886932, 2134609957, 2140349794, 2143934987]:
# print(i,best_or_l(i,True))
score = score + (len(l(i))-len(best_or_l(i,True)))
print("Score:",score)

with open("brute_serious_reverse.json","w") as outfile:
outfile.write(json.dumps(best,sort_keys=True,indent=2))

## Python 3, 34 39 bytes saved

This program simply calculates every number it can reach using simple combinations of the binary and unary operators, which covers 366k out of 4B integers, for a total of a couple of dozen of the test cases. Then I output those results or the trivial solution. This is technically against the rules, because it is certain there is a better solution for some of the cases, but I am confident no one is going to come up with a solution that certainly passes that rule.

Also, I'm just producing all the output at once, because 30 seconds of setup time is bearable once, not 1000 times. The commented out sections increase the runtime significantly while barely reducing the score.

#!/usr/bin/env python3
# -*- coding: cp437 -*-

import math
import gmpy
import json
import random

from seriously import chr_cp437

# MAX=2**31
MAX = 2**31

best = {}

def l(n,force_colon=False):
if force_colon:
return ':'+str(n)
if n>=0 and n<10:
return str(n)
elif n<0 and n>-10:
return str(-n)+chr_cp437(0xF1)
return ':'+str(n)

def l2(n,m):
if n<10 or best_or_l(n)[-1] in "0123456789":
rep = l(n)+best_or_l(m)
else:
rep = best_or_l(n)+best_or_l(m,True)
return rep

def cand(n,rep):
# print(n,rep,len(rep),best[n] if n in best else "")
if n!=int(n):
return False
n=int(n)
if n<=MAX and len(rep)<len(l(n)) and (n not in best or len(rep)<len(best[n])):
best[n] = rep
return True
return False

def best_or_l(n,force_colon=False):
if n in best:
return best[n]
if -n in best and n>0:
return best[-n]+chr_cp437(0xF1)
return l(n,force_colon)

# digits
for i in range(0,10):
best[i]=str(i)

# factorials
for i in range(4,13):
cand(math.factorial(i),l(i)+'!')

# 10**i
for i in range(2,12):
cand(10**i,l(i)+chr_cp437(0xD1))

# 2**i
for i in range(2,32):
cand(2**i,best_or_l(i)+chr_cp437(0xD3))

# a choose b
for a in range(2,1000): # 466 is the highest a for MAX=2**24
for b in range(2,int(a/2+1)):
n = math.factorial(a)/(math.factorial(b)*math.factorial(a-b))
if n>MAX:
break
cand(n,l2(b,a)+chr_cp437(0xDB))

# a P b
for a in range(2,1000): # 257 is the highest a for MAX=2**24
for b in range(2,int(a/2+1)):
n = math.factorial(a)/math.factorial(a-b)
if n>MAX:
break
cand(n,l2(b,a)+chr_cp437(0xDC))

# fibonacci
def fib_formula(n):
golden_ratio = (1 + math.sqrt(5)) / 2
val = (golden_ratio**n - (1 - golden_ratio)**n) / math.sqrt(5)
return int(round(val))
for i in range(3,47):
cand(fib_formula(i),best_or_l(i)+'F')

# i^2 and ^4
for i in range(5,int(math.sqrt(MAX)+1)):
cand(i*i,best_or_l(i)+chr_cp437(0xFD))

# a^b
for a in range(2,int(math.pow(MAX,1.0/3))+1):
for b in range(3,int(math.log(MAX)/math.log(3))+1):
n = a**b
cand(n,l2(b,a)+chr_cp437(0xFC))

# exp(i)
for i in range(3,22):
cand(int(math.ceil(math.exp(i))),best_or_l(i)+'eK')
cand(int(math.floor(math.exp(i))),best_or_l(i)+'eL')

# primes
def primes():
n = 2
while True:
yield n
n = gmpy.next_prime(n)
n = 0
for p in primes():
# print(p)
if p>MAX/1000:
break
rep = best_or_l(n)+'P'
cand(p,rep)
n=n+1

# +1 +2 -1 -2 *2 /2 /4
for key,value in sorted(best.items()):
cand(key+1,value+'u')
cand(key+2,value+chr_cp437(0xA9))
cand(key-1,value+'D')
cand(key-2,value+chr_cp437(0xAA))
cand(key*2,value+chr_cp437(0xE7))
if float(key)/2 == int(float(key)/2):
cand(int((float(key)/2)),value+chr_cp437(0xAB))
cand(int(math.floor(float(key)/2)),value+chr_cp437(0xAB)+'L')
cand(int(math.ceil(float(key)/2)),value+chr_cp437(0xAB)+'K')
if float(key)/4 == int(float(key)/4):
cand(int((float(key)/4)),value+chr_cp437(0xAC))
cand(int(math.floor(float(key)/4)),value+chr_cp437(0xAC)+'L')
cand(int(math.ceil(float(key)/4)),value+chr_cp437(0xAC)+'L')

# bitwise invert
for key,value in sorted(best.items()):
cand(~key,value+'~')

# arithmetic with small second operands
for key,value in sorted(best.items()):
for op in ["+","-","/","/K","\\","*"]:
for i in range(3,10):
if op == "+":
n = key+i
elif op == "-":
n = key-i
elif op == "/":
if i==4:
continue
n = float(key)/i
if int(n)!=n:
continue
n = int(n)
elif op == "/K":
if i==4:
continue
n = int(math.ceil(float(key)/i))
if n == float(key)/i:
continue
elif op == "\\":
if i==4:
continue
n = int(math.floor(float(key)/i))
if n == float(key)/i:
continue
elif op == "*":
n = key*i
rep = value+best_or_l(i)+op
cand(n,rep)

# for key,value in sorted(best.items()):
#     print(key,value)

# def maybe(n,rep):
#     if len(rep)<len(best_or_l(n)):
#         return True
#     return False

# b=[]
# for k in sorted(best.keys()):
#     b.append(k)
#     if k>100000000:
#         break

# def search_for_better(n):
#     if n in best:
#         return best[n]
#     for i in b:
#         if n+i in best:
#             rep = best[n+i]+best[i]+'-'
#             if maybe(n,rep):
#                 return rep
#     for i in b:
#         if n-i in best:
#             rep = best[n-i]+best[i]+'+'
#             if maybe(n,rep):
#                 return rep
#     return l(n)

for key,value in sorted(best.items()):
if random.random()<0.001:
print(key,value)

score = 0
for i in [-2124910654, -2117700574, -2098186988, -2095671996, -2083075613, -2058271687, -2052250777, -2024215903, -2019485642, -2016095616, -2009838326, -2009173317, -2007673992, -2000014444, -1999825668, -1992515610, -1989566707, -1975506037, -1955473208, -1950731112, -1949886423, -1920624450, -1918465596, -1916287469, -1905036556, -1903956118, -1888944417, -1865221863, -1856600057, -1842797147, -1835637734, -1812631357, -1805740096, -1798015647, -1726688233, -1723609647, -1713776890, -1700307138, -1687644479, -1645515069, -1617635994, -1610444000, -1579053372, -1556891649, -1549652116, -1537732956, -1535180388, -1527162056, -1524851611, -1524658412, -1523244369, -1521379172, -1520191198, -1519035741, -1516978241, -1508892332, -1489938422, -1482102944, -1481823232, -1470621147, -1469145091, -1446844485, -1441790509, -1437843276, -1435359182, -1434186947, -1429816311, -1429393781, -1419752032, -1400387846, -1385152926, -1372620863, -1369257355, -1361933674, -1360480816, -1334846204, -1323741718, -1323660173, -1312800992, -1308824840, -1304658551, -1287829999, -1283767920, -1276288210, -1264275838, -1263965596, -1262866901, -1255421887, -1251428680, -1244825786, -1243200329, -1235305532, -1233977691, -1220537074, -1214100716, -1199414474, -1190725823, -1190401800, -1178717689, -1172378149, -1147869245, -1142875190, -1138538768, -1137864183, -1124917489, -1102987222, -1095920186, -1083001017, -1080902655, -1047122002, -1031842676, -1029877334, -1020849489, -1001684838, -998419619, -990915088, -985235989, -982515261, -979074894, -974195629, -973832940, -965324937, -944246431, -938387588, -933873331, -932692878, -928039285, -927947459, -914008773, -907981688, -906376330, -903502449, -898112547, -887444438, -862658502, -843628573, -822463032, -786051095, -776932426, -776033951, -752042328, -746532472, -743149468, -740225710, -734414418, -725435852, -708101516, -699674783, -694869277, -693246525, -690571518, -689249770, -688581912, -686864294, -681445866, -647992869, -641101583, -631409299, -624686189, -613079884, -593711206, -591688546, -591331185, -574790069, -573024823, -565387051, -565137163, -556338668, -556291492, -541411509, -538932064, -500479857, -482419890, -468050561, -424532545, -420534171, -408741873, -406973874, -387664799, -382084509, -367095703, -352332569, -352195997, -346430007, -324596389, -320119776, -306594578, -305952425, -283718911, -267302378, -243302738, -242955859, -232180029, -225394407, -217418127, -212286453, -208344820, -191300139, -186177744, -175765723, -161763935, -157025501, -140389149, -132298608, -126175769, -70566352, -68748576, -53985905, -52674668, -50228620, -39678495, -19825663, -8349922, -8186722, -8125700, -8073135, -8043230, -7994382, -7874433, -7863624, -7784916, -7782477, -7696343, -7607278, -7531250, -7388060, -7368780, -7367625, -7353084, -7334489, -7281141, -7267149, -7140057, -7119066, -7010389, -6992089, -6975258, -6863360, -6784772, -6741079, -6585985, -6550401, -6520011, -6495144, -6459702, -6294273, -6178342, -6169344, -6139663, -6090928, -6022637, -5992707, -5971334, -5925304, -5880940, -5873707, -5807953, -5703992, -5692895, -5535131, -5488812, -5468330, -5404148, -5290247, -5274221, -5264144, -5234715, -5224048, -5179837, -5084014, -5043990, -5028537, -5011679, -4998333, -4922901, -4880159, -4874060, -4787390, -4749096, -4736217, -4502308, -4480611, -4424319, -4363262, -4349743, -4290050, -4240069, -4239657, -4174072, -4093051, -4045363, -4037689, -4033352, -3839265, -3766343, -3716899, -3680075, -3679053, -3581776, -3539227, -3461158, -3282526, -3205947, -3183427, -3169708, -3166430, -3089822, -3061531, -2947574, -2930733, -2919246, -2872882, -2830770, -2739228, -2713826, -2634018, -2613990, -2525529, -2439507, -2432921, -2376201, -2335005, -2307524, -2265548, -2176176, -2123133, -2108773, -2105934, -2075032, -2073940, -2045837, -2045648, -1978182, -1945769, -1935486, -1881608, -1654650, -1602520, -1506746, -1505294, -1475309, -1457605, -1327259, -1312217, -1178723, -1027439, -880781, -833776, -666675, -643098, -593446, -468772, -450369, -443225, -418164, -402004, -319964, -307400, -279414, -190199, -176644, -66862, -32745, -32686, -32352, -32261, -32035, -31928, -31414, -31308, -30925, -30411, -29503, -29182, -28573, -28500, -28093, -27743, -27716, -27351, -27201, -26834, -25946, -25019, -24469, -24341, -24292, -24151, -23732, -22769, -22242, -22002, -20863, -20762, -20644, -20189, -20009, -19142, -19036, -18980, -18616, -18196, -18123, -17942, -17915, -17601, -17494, -16669, -16417, -16317, -15051, -14796, -14742, -14600, -14443, -14159, -14046, -13860, -13804, -13745, -13634, -13498, -13497, -12688, -12471, -12222, -11993, -11467, -11332, -10783, -10250, -10114, -10089, -9930, -9434, -9336, -9128, -9109, -8508, -8460, -8198, -8045, -7850, -7342, -7229, -6762, -6302, -6245, -6171, -5957, -5842, -4906, -4904, -4630, -4613, -4567, -4427, -4091, -4084, -3756, -3665, -3367, -3186, -2922, -2372, -2331, -1936, -1683, -1350, -1002, -719, -152, -128, -127, -124, -122, -121, -119, -116, -113, -112, -111, -107, -104, -102, -101, -100, -95, -94, -91, -90, -87, -81, -80, -79, -78, -73, -72, -69, -68, -66, -65, -63, -57, -54, -52, -51, -48, -47, -46, -45, -43, -41, -37, -33, -31, -30, -27, -25, -21, -18, -15, -12, -8, -1, 0, 1, 3, 4, 5, 6, 11, 14, 17, 23, 25, 26, 27, 28, 29, 31, 32, 39, 41, 46, 49, 51, 52, 56, 58, 61, 64, 66, 67, 70, 74, 79, 80, 86, 88, 89, 92, 93, 99, 102, 104, 109, 113, 117, 120, 122, 123, 127, 695, 912, 1792, 2857, 3150, 3184, 4060, 4626, 5671, 6412, 6827, 7999, 8017, 8646, 8798, 9703, 9837, 10049, 10442, 10912, 11400, 11430, 11436, 11551, 11937, 12480, 13258, 13469, 13689, 13963, 13982, 14019, 14152, 14259, 14346, 15416, 15613, 15954, 16241, 16814, 16844, 17564, 17702, 17751, 18537, 18763, 19890, 21216, 22238, 22548, 23243, 23383, 23386, 23407, 23940, 24076, 24796, 24870, 24898, 24967, 25139, 25176, 25699, 26167, 26536, 26614, 27008, 27087, 27142, 27356, 27458, 27800, 27827, 27924, 28595, 29053, 29229, 29884, 29900, 30460, 30556, 30701, 30815, 30995, 31613, 31761, 31772, 32099, 32308, 32674, 75627, 80472, 103073, 110477, 115718, 172418, 212268, 242652, 396135, 442591, 467087, 496849, 675960, 759343, 846297, 881562, 1003458, 1153900, 1156733, 1164679, 1208265, 1318372, 1363958, 1411655, 1522329, 1559609, 1677118, 1693658, 1703597, 1811223, 1831642, 1838628, 1884144, 1931545, 2085504, 2168156, 2170263, 2239585, 2308894, 2329235, 2364957, 2432335, 2435551, 2596936, 2684907, 2691011, 2705195, 2738057, 2851897, 2925289, 2995414, 3051534, 3216094, 3267022, 3271559, 3338856, 3440797, 3638325, 3651369, 3718696, 3724814, 3811069, 3854697, 3866969, 3893228, 3963455, 3984546, 4098376, 4100957, 4128113, 4200719, 4256344, 4286332, 4306356, 4316314, 4438803, 4458063, 4461638, 4552228, 4563790, 4584831, 4607992, 4884455, 4907501, 5045419, 5066844, 5150624, 5157161, 5190669, 5314703, 5337397, 5434807, 5440092, 5502665, 5523089, 5547122, 5566200, 5582936, 5634068, 5690330, 5776984, 5778441, 5818505, 5826687, 5827184, 5885735, 6010506, 6084254, 6131498, 6138324, 6250773, 6292801, 6306275, 6315242, 6331640, 6484374, 6502969, 6545970, 6666951, 6690905, 6763576, 6766086, 6895048, 6912227, 6929081, 6941390, 6978168, 7045672, 7085246, 7193307, 7197398, 7270237, 7276767, 7295790, 7375488, 7472098, 7687424, 7840758, 7880957, 7904499, 7948678, 7974126, 8015691, 8037685, 8112955, 8131380, 8140556, 8142384, 8220436, 8308817, 8331317, 22581970, 45809129, 48103779, 78212045, 79674901, 97299830, 110308649, 131744428, 136663461, 138485719, 139842794, 152061792, 152685704, 153070991, 156228213, 164884737, 174776199, 189346581, 193148547, 208582124, 223891881, 227308187, 237373798, 241214067, 242476929, 245495851, 260606593, 275202667, 285717038, 317009689, 322759532, 325369206, 339724742, 340122632, 345010859, 352375176, 355826263, 359695034, 366118516, 370008270, 382712922, 386379440, 401153345, 404986391, 426084981, 442843409, 473909474, 475192613, 492302667, 494747879, 506279889, 509813998, 537558350, 548423414, 548467404, 566383324, 574188786, 574792333, 591678147, 596558084, 597423476, 602432742, 603067874, 629552047, 630893263, 635249783, 644959276, 650710927, 664859367, 669433203, 684329599, 699991513, 714451929, 723556530, 739294558, 750895264, 757618344, 781123405, 796973385, 801637715, 804776709, 829003666, 829219068, 840167037, 854882202, 860066192, 864304878, 864808449, 867107161, 871871263, 880591851, 883020336, 883178082, 920223781, 936008673, 939417822, 956776353, 958281059, 962183717, 964059257, 967860573, 974322643, 974999286, 980009921, 1032949015, 1044249483, 1064892676, 1075628270, 1080848022, 1085571657, 1173635593, 1174809080, 1176744978, 1209783795, 1212074975, 1252323507, 1254757790, 1301450562, 1302240953, 1314501797, 1315121266, 1339304157, 1364304289, 1376260506, 1383883477, 1395158643, 1411117754, 1440755058, 1448365702, 1466814914, 1468433821, 1490105126, 1493912601, 1495600372, 1509536621, 1511014977, 1545693948, 1548924199, 1566583103, 1569747154, 1574097219, 1597784674, 1610710480, 1618324005, 1646105187, 1649417465, 1655649169, 1660619384, 1668826887, 1671093718, 1672456990, 1673477565, 1678638502, 1682302139, 1682515769, 1687920300, 1690062315, 1706031388, 1713660819, 1772170709, 1778416812, 1833443690, 1861312062, 1876004501, 1876358085, 1882435551, 1916050713, 1944906037, 1950207172, 1951593247, 1973638546, 1976288281, 1994977271, 2020053060, 2025281195, 2029716419, 2033980539, 2052482076, 2058251762, 2069273004, 2073978021, 2111013213, 2119886932, 2134609957, 2140349794, 2143934987]:
print(i)
print(best_or_l(i,True))
score = score + (len(l(i))-len(best_or_l(i,True)))
print("Score:",score)

# print(len(best))

with open("aim.json","w") as outfile:
outfile.write(json.dumps(best,sort_keys=True,indent=2))

Here's a random sampling of the sorts of Actually programs that end up found by this algorithm:

15875 49█²D
178085 :422²u
6195119 :2489²¬
11276166 :3358²⌐
14516098 :3810²¬
32924643 :5738²D
35003345 :8367²½K
66438802 :8151²u
95664294 3:363ⁿτ
100915813 3:847█¬
111894084 :10578²
219662043 :14821²⌐
220849321 :14861²
236390625 :15375²
282710596 :16814²
296511180 :34439²¼L
375584401 :19380²u
460188303 :21452²D
465157056 :43135²¼L
509991890 :22583²u
510963420 :45209²¼L
606981768 :24637²D
659407868 8FeK½K
697212482 :18671²τ
805764994 :28386²¬
852225612 :41285²½L
941078331 :30677²⌐
1034715540 :45491²½L
1193771602 :34551²u
1326125054 :36416²¬
2030403600 :45060²
2078904023 :45595²¬
• @KevinLau-notKenny score in this challenge is the total size of the output, the thousand Actually programs, not the size of the Python program – Sparr May 18 '16 at 3:37
• I like this approach. I'm willing to be a bit more flexible with the time restriction and the must-do-better-than-trivial rule if it allows for more interesting solutions - I mainly wanted to avoid untestable brute-force solutions that run for centuries and the trivial solution of "prepend a :", which is unimaginative and goes against the spirit of the challenge. – Mego May 18 '16 at 4:21
• I've modified the requirements so that solutions only have to do at least as well as the trivial solution, rather than better if possible, and increased the time limit to 30 seconds per input. Your solution is now valid, and you may be able to make some additional improvements with the relaxed requirements. – Mego May 18 '16 at 5:45